{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "16011208-5b64-463b-b5a4-c506370f9914",
   "metadata": {},
   "source": [
    "Chapter 20\n",
    "# 三种天气状况，随机行走\n",
    "Book_6《数据有道》 | 鸢尾花书：从加减乘除到机器学习"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "db98e7ed-fcf5-4c2b-a3ea-455128abbf60",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f00987b7-f938-4634-91e5-7cbdd729527b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate_markov_chain(T, initial_state, num_steps):\n",
    "\n",
    "    states = [initial_state]  \n",
    "    # 初始状态\n",
    "    \n",
    "    current_state = initial_state\n",
    "    \n",
    "    for _ in range(num_steps):\n",
    "        # 根据当前状态和转移矩阵决定下一状态\n",
    "        next_state = np.random.choice(np.arange(len(T)), \n",
    "                                      p=T[current_state])\n",
    "        states.append(next_state)\n",
    "        current_state = next_state\n",
    "        \n",
    "    states = np.array(states)\n",
    "    return states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d93ea256-755e-478a-82be-0ddbe52ad6b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 定义转移矩阵\n",
    "T = np.array([[0.70, 0.45, 0.55],  \n",
    "              [0.25, 0.30, 0.30],\n",
    "              [0.05, 0.25, 0.15]]) \n",
    "\n",
    "# 模拟马尔科夫链\n",
    "initial_state = 0  # 假设初始状态为 0\n",
    "num_steps = 300    # 假设模拟步数\n",
    "states = simulate_markov_chain(T.T, initial_state, num_steps)\n",
    "\n",
    "indices = np.arange(num_steps + 1)\n",
    "labels = [\"Sun\", \"Cloud\", \"Rain\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "65066ecd-5814-4706-bf33-57f939b4aa95",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 3))\n",
    "plt.plot(indices, states, c = '0.8')\n",
    "\n",
    "for state_i,label_i in zip([0, 1, 2],labels):\n",
    "    plt.scatter(indices[states == state_i], \n",
    "                states[states == state_i],\n",
    "                label=label_i)\n",
    "# plt.legend()\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('State')\n",
    "plt.yticks([0, 1, 2], labels)\n",
    "plt.grid(True)\n",
    "plt.savefig('马尔科夫链随机行走.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b18c1633-de6a-4745-a8b9-408fcd806556",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b09c2d10-37af-43e8-a8b6-b6d3a78b946a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 计算0, 1, 2的累积出现频率\n",
    "cumulative_counts = np.cumsum(np.eye(3)[states], axis=0)\n",
    "cumulative_probs = cumulative_counts / np.arange(1, len(states) + 1).reshape(-1, 1)\n",
    "\n",
    "# 绘制累积概率随时间的变化图\n",
    "plt.figure(figsize=(8, 3))\n",
    "plt.plot(cumulative_probs, label=labels)\n",
    "\n",
    "plt.xlabel(\"Iteration\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.savefig('累积概率曲线.svg')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "3f686068-9350-4ee7-a570-fbf8131cf4d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.61333333, 0.24666667, 0.14333333])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob_list = counts_list/num_steps\n",
    "prob_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ede17897-7158-44d5-b995-a3921e88b5d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "states_list, counts_list = np.unique(states, return_counts=True)\n",
    "\n",
    "plt.figure(figsize=(5, 3))\n",
    "plt.bar(states_list,prob_list)\n",
    "plt.xticks(states_list)\n",
    "plt.xticks([0, 1, 2], labels)\n",
    "plt.savefig('最终结果.svg')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
